2018/05/31 by Stefano Gogioso, Dan Marsden, Bob Coecke
Physics and Astronomy · Mathematics · #quant-ph #math.CT
paper · pdf · doi:10.4204/eptcs.287.10
published as EPTCS 287, 2019, pp. 179-190 · In Proceedings QPL 2018, arXiv:1901.09476
arxiv created 2019/01/29 · arxiv updated 2019/01/30
In previous work we proved that, for categories of free finite-dimensional modules over a commutative semiring, linear compact-closed symmetric monoidal structure is a property, rather than a structure. That is, if there is such a structure, then it is uniquely defined (up to monoidal equivalence). Here we provide a novel unifying category-theoretic notion of symmetric monoidal structure with local character, which we prove to be a property for a much broader spectrum of categorical examples, including the infinite-dimensional case of relations over a quantale and the non-free case of finitely generated modules over a principal ideal domain.